The need for efficient image reconstruction and interpretation is still a challenge in many fields. In spite of methods and algorithms that have been proposed, there is a need to improve the performance. Among the existing methods are the standard 2D Fourier transform, the Wavelet with its different modified versions or the total variations based approach. More recently, methods based on partial differential equations have been proposed. Many other algorithms have been proposed, each method having its advantages and limitations.
A signal can be decomposed using a family of functions, which can be given by squared eigenfunctions associated to the discrete spectrum of a semi-classical Schrödinger operator where the signal can be considered as a potential of such operator. This decomposition can be applied to one-dimensional signals such as arterial blood pressure signals or machinery performance signals.